CN108921349B - Method for predicting question making error position based on Bayesian network - Google Patents
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Abstract
The invention relates to the technical field of machine learning, and discloses a method for predicting question making error positions based on a Bayesian network. The invention provides an estimation method which can ensure the accuracy of the performance of making questions or the prediction of wrong positions of making questions for a responder while minimizing the labor cost, and further can provide more accurate information for the targeted explanation, namely compared with the similar methods, the estimation accuracy rate of the detailed step level can be provided, so that the performance of the current student on the question can be more effectively predicted, and the completion condition of the current student is evaluated, rather than the traditional rough question level accuracy and error. In addition, the method can correct the current estimation by collecting more facts, so the number and the types of the facts needing to be collected can be flexibly adjusted according to the required precision, and the method is basically not limited by application scenes.
Description
Technical Field
The invention belongs to the technical field of machine learning, and particularly relates to a method for predicting question making error positions based on a Bayesian network, which can be applied to the education industry.
Background
In the education industry, the performance prediction of students on each topic and the accurate evaluation of the actual performance of students on the topics are very important for more targeted explanation of students.
This is typically done by an instructor in a conventional manner. Teachers with rich experience can effectively locate error-prone points of one subject. However, the teacher analyzes every question, which consumes a lot of manpower, and considering the current ratio of teacher to student, one practical teacher often takes charge of a plurality of students, so that it is difficult to clearly remember the specific situation of each student, and the predicted or estimated wrong position of the question given finally is closer to the average level of most students.
The conventional automatic prediction directly evaluates the accuracy of the completion of the subject according to the abilities of students and the abilities required by the subject. The evaluation mode solves the problem of manpower, can complete evaluation without human intervention, only considers the content coverage related to the subject, but does not consider the influence of the structure of the subject, so the accuracy of the evaluation result is low. Meanwhile, the scheme can only estimate the accuracy of the student on the whole subject, but cannot more specifically estimate which problems occur in the problem solving process, so that the utilization value of the result is not high even if the evaluation is finished.
At present, an independent analysis scheme is developed for each topic, and judgment is performed one by one according to interaction results of students in a current topic scene, so that a position of a wrong topic is determined. But also has a number of disadvantages: firstly, the scheme cannot give meaningful results under the condition that a user does not provide any interactive results, secondly, a large amount of human resources are needed for developing a special analysis scheme for each topic, although the scheme looks like a whole and a whole, the development of the scheme simultaneously needs technical resources and teaching resources, and the topic has no reusable content, so that the development cost is high, and the scheme is basically impossible to be used in real products.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention aims to provide a method for predicting a problem-making error location based on a bayesian network.
The technical scheme adopted by the invention is as follows:
a method for predicting question error positions based on a Bayesian network comprises the following steps:
s100, pre-storing current ability data of an responder and basic data of test questions of the responder in a database, wherein the current ability data of the responder comprises current ability values of the responder at each knowledge point, and the basic data of the test questions comprises standard answers with at least two answering steps, topological sequences for expressing the prior-posterior relations of all the answering steps, and knowledge points, knowledge point difficulty values and knowledge point discrimination values corresponding to each answering step;
s101, aiming at each answering step of answering test questions, calculating to obtain corresponding individual pair prediction probability according to the current ability data of an answering person and the basic data of the test questions;
s102, constructing a Bayesian network according to the topological sequence of the answer questions, enabling each network node to correspond to one answer step, and marking the occurrence events of the network nodes as 'answer-to-answer step';
s103, for all non-initial network nodes with the degree of entry not being 0 in the Bayesian network, performing point splitting according to the following mode: splitting the network node into a prior network node A and a posterior network node B which have a prior-posterior relationship, marking the occurrence of the prior network node A as 'all conditions of the corresponding solution step are complete', marking the occurrence of the posterior network node B as 'doing the corresponding solution step', and setting the posterior probability of the posterior network node B as the independent doing the corresponding prediction probability of the corresponding solution step;
setting corresponding prior probability as the independent pair prediction probability of the corresponding answer step aiming at all initial network nodes with the degree of incidence of 0 in the Bayesian network;
s104, according to the known fact state of the partial solution step, setting the known fact state in the Bayesian network, wherein the occurrence event is the determined occurrence probability of the corresponding network node which makes the corresponding solution step, and the known fact state is the verification success or the verification failure;
s105, solving the Bayesian network, and deducing the estimated occurrence probability of each network node which is not provided with the determined occurrence probability, wherein the network node which is not provided with the determined occurrence probability corresponds to the solving step of the undetermined known fact state;
s106, for each solution step of undetermined known fact state, calculating the prediction probability of just making a mistake in the corresponding solution step according to the following formula:
in the formula, pAEstimated probability of occurrence, p, of the prior network node A for the corresponding solution stepBThe estimated occurrence probability of the posterior network node B corresponding to the answering step is p, and the estimated occurrence probability of the initial network node corresponding to the answering step is p.
Preferably, in the step S101, the method for calculating the individual pair prediction probability of the solution step according to the current ability data of the responder and the basic data of the test questions comprises the following steps:
and searching the knowledge point, the knowledge point difficulty value and the knowledge point discrimination value corresponding to the answering step from the test question basic data, searching the current capability value of the answer in the knowledge point corresponding to the answering step from the current capability data of the answer, inputting the current capability value, the knowledge point difficulty value and the knowledge point discrimination value into an IRT mathematical model, and taking the output probability of the IRT mathematical model as the independent pair prediction probability corresponding to the answering step. Specifically, the IRT mathematical model is a 3-parameter Normal-objective model or a 3-parameter Logistic model.
Preferably, the step S104 includes the following steps:
aiming at the solution step with the known fact state as the verification success, the determined occurrence probability of the network node which is arranged in the Bayesian network and has the occurrence event of 'doing the corresponding solution step' is 100 percent;
for the solution step with the known fact state as the verification failure, the determined occurrence probability of the network node which is arranged in the Bayesian network and has the occurrence event of 'doing the corresponding solution step' is 0%.
Preferably, before the step S104, the method further includes the following steps:
and for the answering step of which the new marked known fact state is checked successfully, the current ability value of the responder at the knowledge point corresponding to the answering step is adjusted up, and then the current ability data of the responder is updated and stored.
Preferably, before the step S104, the method further includes the following steps:
and aiming at the answering step of which the new marked known fact state is failed to check, adjusting the current ability value of the responder at the knowledge point corresponding to the answering step, and then updating and storing the current ability data of the responder.
Further optimally, after updating and storing the responder current capacity data, the steps S101 to S103 are executed again.
Preferably, after the step S106, the method further includes the following steps:
s107, corresponding prediction probability PERThe maximum solution step is used as the preferred problem error position.
Preferably, after the step S106, the method further includes the following steps:
and S108, through man-machine interaction, if the answer step of the new marked known fact state exists, returning to execute the steps S104-S106.
Preferably, the test question basic data further comprises question content, a question solving skill corresponding to at least one answer step and/or a weight coefficient corresponding to each answer step.
The invention has the beneficial effects that:
(1) the invention provides an estimation method which can ensure the performance of questions on a responder or the prediction accuracy of wrong positions of the questions while minimizing the labor cost, thereby providing more accurate information for the targeted explanation;
(2) compared with the similar method, the method can provide the estimation accuracy rate of detail to step level, thereby being capable of more effectively predicting the performance of the current student on the subject and evaluating the completion condition of the current student instead of the traditional rough subject level accuracy and error;
(3) the method fully considers the influence of the step structure in the question on the accuracy in the prediction, so that the result obtained by the method is more accurate compared with the traditional method;
(4) according to the method, a large amount of manual interference is not needed, and only the questions are set according to the dependency relationship among the steps, so that effective evaluation can be performed for any student without human intervention, and excessive labor cost is avoided;
(5) the method can correct the current estimation by collecting more facts, so the number and the types of the facts needing to be collected can be flexibly adjusted according to the required precision, and the method is basically not limited by application scenes.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for predicting a problem-making error position based on a bayesian network according to the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments. It should be noted that the description of the embodiments is provided to help understanding of the present invention, but the present invention is not limited thereto.
The term "and/or" herein is merely an association describing an associated object, meaning that three relationships may exist, e.g., a and/or B, may mean: a exists alone, B exists alone, and A and B exist at the same time, and the term "/and" is used herein to describe another association object relationship, which means that two relationships may exist, for example, A/and B, may mean: a alone, and both a and B alone, and further, the character "/" in this document generally means that the former and latter associated objects are in an "or" relationship.
Example one
As shown in fig. 1, the method for predicting a problem error location based on a bayesian network provided in this embodiment includes the following steps.
S100, current ability data of an answering machine and basic data of test questions of the answering machine are stored in a database in advance, wherein the current ability data of the answering machine comprise current ability values of the answering machine at all knowledge points, and the basic data of the test questions comprise standard answers with at least two answering steps, topological sequences used for expressing the prior-posterior relations of all the answering steps, knowledge points corresponding to each answering step, difficulty values of the knowledge points and discrimination values of the knowledge points.
In the step S100, the checking relationship between the solution step and the answer step means that for the solution step a and the answer step b, if the solution step a must be performed first and then the solution step b must be performed, the solution step a and the answer step b have a posterior-to-anterior relationship: the solution step a is a prior step, and the solution step b is a posterior step. Therefore, a topological order which has a certain topological network structure and expresses the a-priori and a-posteriori relationships of all the solution steps can be obtained. In addition, optimally, the test question basic data can also comprise question contents, a question solving skill corresponding to at least one answer step, a weight coefficient corresponding to each answer step and the like.
S101, aiming at each answering step of the answering test questions, calculating to obtain corresponding individual pair prediction probability according to the current ability data of the answering person and the basic data of the test questions.
In the step S101, the individual pair prediction probability refers to the probability that the responder correctly answers the solution step when the conditions required by the solution step (for example, all prior steps preceding the topological order) are complete. Optimized, the method for calculating the prediction probability of the solution step by doing the pair alone may include, but is not limited to, the following steps: and searching the knowledge point, the knowledge point difficulty value and the knowledge point discrimination value corresponding to the answering step from the test question basic data, searching the current capability value of the answer in the knowledge point corresponding to the answering step from the current capability data of the answer, inputting the current capability value, the knowledge point difficulty value and the knowledge point discrimination value into an IRT mathematical model, and taking the output probability of the IRT mathematical model as the independent pair prediction probability corresponding to the answering step.
The IRT mathematical model is an existing mathematical model based on an IRT Theory (Item Response Theory, also called topic Response Theory or latent trait Theory, which is a collective name of a series of psychology models) and used for analyzing test results or questionnaire survey data. Specifically, the IRT mathematical model may be, but not limited to, a 3-parameter Normal-objective model or a 3-parameter Logistic model.
S102, constructing a Bayesian network according to the topological sequence of the answer questions, enabling each network node to correspond to one answer step, and marking the occurrence events of the network nodes as 'answer to corresponding steps'.
In step S102, the bayesian network is based on bayesian theory and is a topological network structure composed of a Directed Acyclic Graph (DAG) and a Conditional Probability Table (CPT), which represents a set of random variables and their conditional dependencies through a directed acyclic graph, and is parameterized through a conditional probability distribution, each network node is parameterized through P (node | pa (node)), and pa (node) represents a prior node in the bayesian network, so that the topological network structure of the initial bayesian network is completely consistent with the topological sequence of the solution questions, and the corresponding conditional probability of the network node of the initial bayesian network is "the probability of correctly answering the solution step given the results of all the dependent solution steps", that is, the prediction probability of the solution step alone.
S103, for all non-initial network nodes with the degree of entry not being 0 in the Bayesian network, performing point splitting according to the following mode: splitting the network node into a prior network node A and a posterior network node B which have a prior-posterior relationship, marking the occurrence of the prior network node A as 'all conditions of the corresponding solution step are complete', marking the occurrence of the posterior network node B as 'doing the corresponding solution step', and setting the posterior probability of the posterior network node B as the independent doing the corresponding prediction probability of the corresponding solution step; and setting corresponding prior probability as the independent pair prediction probability of the corresponding solution step aiming at all initial network nodes with the degree of incidence of 0 in the Bayesian network.
In step S103, the prior event of the prior network node a is a posterior network node B or an initial network node of other solution steps that are depended on by the corresponding solution step, and when all the prior events occur, the conditional probability of the prior network node a is 100%, otherwise, the conditional probability is 0%. The prior event of the posterior network node B is the prior network node a corresponding to the same answer step, so when the event of the prior network node a occurs, the conditional probability (i.e., posterior probability) of the posterior network node B is the individual pair prediction probability corresponding to the answer step, and when the event of the prior network node a does not occur, the conditional probability of the posterior network node B is 0%.
S104, according to the known fact state of the partial solution step, the determined occurrence probability of the corresponding network node is set in the Bayesian network, and the occurrence event is 'doing the corresponding solution step', wherein the known fact state is checking success or checking failure.
In the step S104, the known fact state is used to identify a confirmation result of the responder in the corresponding answering step through human-computer interaction, wherein the successful verification indicates that the responder reads the answer of the corresponding answering step and confirms that the answering step is right; the failure of checking means that the responder read the answer corresponding to the answering step and confirms that the answering step is wrong. Further, the known fact state may also be a state in which: the verification fails, which is used for indicating that the responder compares the conclusion of the corresponding answer step, but the conclusion is inconsistent with the conclusion of the final answer, namely the answer step has a question; and reading the answers, wherein the answers are used for indicating that the answerer does not answer the corresponding answering step and only reads the answers of the answering step.
Since the right or wrong partial solution step reflects the current ability value of the responder at the corresponding knowledge point, in order to further improve the prediction accuracy, before the step S104, the following steps are preferably included: aiming at the answering step of newly marking the known fact state as successful verification, the current ability value of the answering person at the knowledge point corresponding to the answering step is adjusted up, and then the current ability data of the answering person is updated and stored; and aiming at the answering step of which the new marked known fact state is failed to check, adjusting the current ability value of the responder at the knowledge point corresponding to the answering step, and then updating and storing the current ability data of the responder. And after updating and storing the current capability data of the responder, re-executing the steps S101 to S103.
In the step S104, the optimization may include, but is not limited to, the following steps:
aiming at the solution step with the known fact state as the verification success, the determined occurrence probability of the network node which is arranged in the Bayesian network and has the occurrence event of 'doing the corresponding solution step' is 100 percent;
for the solution step with the known fact state as the verification failure, the determined occurrence probability of the network node which is arranged in the Bayesian network and has the occurrence event of 'doing the corresponding solution step' is 0%.
Thus, with the aforementioned arrangement, for the answering step that the responder has done the answer, the meaning in the bayesian network thereof can represent that the event corresponding to the posterior network node B finally occurs (the determined occurrence probability is 100%); by the same way, it can be shown that the event corresponding to the posterior network node B does not finally occur (the determined occurrence probability is 0%). If there are no facts at all (i.e., there are no solution steps for which the fact state is known to be a check success or a check failure), then the result of the evaluation is the probability that the responder will make each solution step; if there are already partial facts (i.e., there are solution steps whose factual state is known to be either verification successful or verification failed), then the result of the evaluation is the conditional probability of doing the solution step for each given fact as a condition.
And S105, solving the Bayesian network, and deducing the estimated occurrence probability of each network node which is not provided with the determined occurrence probability, wherein the network node which is not provided with the determined occurrence probability corresponds to the solving step of the undetermined known fact state.
In step S105, the algorithm for solving the bayesian network is an existing algorithm. The estimated occurrence probability is the prediction probability of the prior solution step before the corresponding solution step or the topological sequence.
S106, for each solution step of undetermined known fact state, calculating the prediction probability of just making a mistake in the corresponding solution step according to the following formula:
in the formula, pAEstimated probability of occurrence, p, of the prior network node A for the corresponding solution stepBThe estimated occurrence probability of the posterior network node B corresponding to the answering step is p, and the estimated occurrence probability of the initial network node corresponding to the answering step is p.
Thus, through the steps S100 to S106, the following three probabilities can be obtained: the respondent makes the prediction probability of each answer step independently, and the responder has no error until each answer step without determining the known factual state (i.e. the respondent makes the prediction probability of each answer step or the respondent makes the prediction probability according to the topological sequence orderThe predictive probabilities for which the a priori solution steps preceding the corresponding solution step are all paired) and the predictive probabilities for which the respondent made a mistake in each solution step corresponding to an undetermined known fact state. Based on the three probabilities, the error probability of the respondent in each answering step can be calculated, so that the method can be widely applied to any occasions needing to express prediction on the subjects for students. Furthermore, it is optimized that, after the step S106, the following steps are further included: s107, corresponding prediction probability PERThe maximum value solution step is used as a first choice of the error position of the question, and the error position of the question can be accurately positioned.
Optimally, in order to update the output result in time, after the step S106, the following steps are further included: and S108, through man-machine interaction, if the answer step of the new marked known fact state exists, returning to execute the steps S104-S106.
In summary, the method for predicting the error position of the question based on the bayesian network provided by the embodiment has the following technical effects:
(1) the embodiment provides an estimation method which can ensure the performance of questions on a responder or the prediction accuracy of wrong positions of the questions while minimizing the labor cost, and further can provide more accurate information for the targeted explanation;
(2) compared with the similar method, the method can provide the estimation accuracy rate of detail to step level, thereby being capable of more effectively predicting the performance of the current student on the subject and evaluating the completion condition of the current student instead of the traditional rough subject level accuracy and error;
(3) the method fully considers the influence of the step structure in the question on the accuracy in the prediction, so that the result obtained by the method is more accurate compared with the traditional method;
(4) according to the method, a large amount of manual interference is not needed, and only the questions are set according to the dependency relationship among the steps, so that effective evaluation can be performed for any student without human intervention, and excessive labor cost is avoided;
(5) the method can correct the current estimation by collecting more facts, so the number and the types of the facts needing to be collected can be flexibly adjusted according to the required precision, and the method is basically not limited by application scenes.
The present invention is not limited to the above-described alternative embodiments, and various other forms of products can be obtained by anyone in light of the present invention. The above detailed description should not be taken as limiting the scope of the invention, which is defined in the claims, and which the description is intended to be interpreted accordingly.
Claims (10)
1. A method for predicting question error positions based on a Bayesian network is characterized by comprising the following steps:
s100, pre-storing current ability data of an responder and basic data of test questions of the responder in a database, wherein the current ability data of the responder comprises current ability values of the responder at each knowledge point, and the basic data of the test questions comprises standard answers with at least two answering steps, topological sequences for expressing the prior-posterior relations of all the answering steps, and knowledge points, knowledge point difficulty values and knowledge point discrimination values corresponding to each answering step;
s101, aiming at each answering step of answering test questions, calculating to obtain corresponding individual pair prediction probability according to the current ability data of an answering person and the basic data of the test questions;
s102, constructing a Bayesian network according to the topological sequence of the answer questions, enabling each network node to correspond to one answer step, and marking the occurrence events of the network nodes as 'answer-to-answer step';
s103, for all non-initial network nodes with the degree of entry not being 0 in the Bayesian network, performing point splitting according to the following mode: splitting the network node into a prior network node A and a posterior network node B which have a prior-posterior relationship, marking the occurrence of the prior network node A as 'all conditions of the corresponding solution step are complete', marking the occurrence of the posterior network node B as 'doing the corresponding solution step', and setting the posterior probability of the posterior network node B as the independent doing the corresponding prediction probability of the corresponding solution step;
setting corresponding prior probability as the independent pair prediction probability of the corresponding answer step aiming at all initial network nodes with the degree of incidence of 0 in the Bayesian network;
s104, according to the known fact state of the partial solution step, setting the known fact state in the Bayesian network, wherein the occurrence event is the determined occurrence probability of the corresponding network node which makes the corresponding solution step, and the known fact state is the verification success or the verification failure;
s105, solving the Bayesian network, and deducing the estimated occurrence probability of each network node which is not provided with the determined occurrence probability, wherein the network node which is not provided with the determined occurrence probability corresponds to the solving step of the undetermined known fact state;
s106, for each solution step of undetermined known fact state, calculating the prediction probability of just making a mistake in the corresponding solution step according to the following formula:
in the formula, pAEstimated probability of occurrence, p, of the prior network node A for the corresponding solution stepBThe estimated occurrence probability of the posterior network node B corresponding to the answering step is p, and the estimated occurrence probability of the initial network node corresponding to the answering step is p.
2. The method according to claim 1, wherein the step S101 of calculating the individual pair prediction probability of the solution step according to the current capability data of the respondent and the basic data of the test questions comprises the steps of:
and searching the knowledge point, the knowledge point difficulty value and the knowledge point discrimination value corresponding to the answering step from the test question basic data, searching the current capability value of the answer in the knowledge point corresponding to the answering step from the current capability data of the answer, inputting the current capability value, the knowledge point difficulty value and the knowledge point discrimination value into an IRT mathematical model, and taking the output probability of the IRT mathematical model as the independent pair prediction probability corresponding to the answering step.
3. The method of claim 2, wherein the IRT mathematical model is a 3-parameter Normal-objective model or a 3-parameter Logistic model.
4. The method of claim 1, wherein the step S104 comprises the steps of:
aiming at the solution step with the known fact state as the verification success, the determined occurrence probability of the network node which is arranged in the Bayesian network and has the occurrence event of 'doing the corresponding solution step' is 100 percent;
for the solution step with the known fact state as the verification failure, the determined occurrence probability of the network node which is arranged in the Bayesian network and has the occurrence event of 'doing the corresponding solution step' is 0%.
5. The method of claim 1, wherein before the step S104, the method further comprises the following steps:
and for the answering step of which the new marked known fact state is checked successfully, the current ability value of the responder at the knowledge point corresponding to the answering step is adjusted up, and then the current ability data of the responder is updated and stored.
6. The method of claim 1, wherein before the step S104, the method further comprises the following steps:
and aiming at the answering step of which the new marked known fact state is failed to check, adjusting the current ability value of the responder at the knowledge point corresponding to the answering step, and then updating and storing the current ability data of the responder.
7. The method for predicting the position of the question error based on the Bayesian network as recited in claim 5 or 6, wherein the steps S101 to S103 are re-executed after the current ability data of the responder is updated and stored.
8. The method of claim 1, wherein after the step S106, the method further comprises the steps of:
s107, corresponding prediction probability PERThe maximum solution step is used as the preferred problem error position.
9. The method of claim 1, wherein after the step S106, the method further comprises the steps of:
and S108, through man-machine interaction, if the answer step of the new marked known fact state exists, returning to execute the steps S104-S106.
10. The method of claim 1, wherein the basic data of questions further comprises the contents of questions, the skills of solving the questions corresponding to at least one solution step and/or the weight coefficient corresponding to each solution step.
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